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Oligopoly and Oligopsony in International Trade∗
Luca Macedoni†
Aarhus University
Vladimir Tyazhelnikov‡
The University of Sydney
October 2018
Abstract
Large firms dominate final goods markets, in which they have oligopoly power,
and also input markets, in which they have oligopsony power. Using data on market
concentration, we find that both oligopoly and oligopsony power increase unit prices
of export goods. We investigate the effects of international trade on the two sources of
firms’ market power and prices, in a theoretical model in which firms are oligopolists
in the market for final goods and oligopsonists in the market for inputs. International
integration in final goods markets reduces oligopoly power but it has the opposite effect
on oligopsony power. Similarly, input market integration reduces oligopsony power, but
it increases oligopoly power.
JEL Classification: F12, F13.
Keywords: Oligopoly, Oligopsony, Market Power, Market Concentration.
∗We thank Robert Feenstra and John Romalis for early suggestion, support, and for providing the data.We also thank seminar participants at Aarhus University, ETSG and University of New South Wales.†[email protected]‡[email protected]
1 Introduction
Large firms dominate trade flows, as a small number of the largest exporters accounts for most
of countries’ total exports (Freund and Pierola, 2015) and imports (Bernard et al., 2016). A
growing body of literature has explored the effects of market power in final goods markets,
where large firms act as oligopolists. Oligopolies affect the welfare of consumers: the larger
the market power of oligopolists, the larger their markups (Atkeson and Burstein, 2008)
and the smaller the number of varieties they export (Eckel and Neary, 2010). International
competition across oligopolists reduces their market power, generating gains from a reduction
of markups (Edmond et al., 2015), and from expanding the number of varieties exported per
firm (Macedoni, 2017).
Firms are not only large in the market for final goods, but also in the market for factors
of production (Azar et al., 2017; Morlacco, 2017).1 However, little is known on the effects of
trade in the presence of firm’s market power in the market for factors of production. When
there are few large buyers, the market is known as a oligopsony: each buyer restricts its
demand in an effort to keep prices low (Boal and Ransom, 1997). The extent by which
buyers restrict their demand is what we call oligopsony power. The goal of this paper is to
study the effects of oligopsony and oligopoly power on firms’ prices, and how international
integration affect oligopsony and oligopoly power.
To investigate the effects of the two sources of market power on prices, we use a rich
data set on unit prices from WITS and on market concentration from Feenstra and We-
instein (2017) for a wide set of countries and industries. We proxy both oligopsony and
oligopoly power using appropriately defined Herfindahl Indexes. Our main empirical finding
is that both higher oligopsony power and oligopoly power increases prices of export goods.
Moreover, the quantitative effects of oligopsony power dominate those of oligopoly power.
In particular, an increase in input market concentration by a standard deviation increases
markups by 1% to 10% while an increase in one standard deviation on final goods market
concentration increases markups by 0 to 1%. The empirical results are robust to a number
of alternative specifications and definitions of market concentration.
To understand the effects of international integration on the two sources of market power,
we build a general equilibrium model in which few large, homogeneous firms produce differ-
entiated goods, competing oligopolistically. Moreover, firms employ an input, the market of
which is oligopsonistic. Such an input could be thought as specialized labor, capital, raw
materials, or some intermediate input. Firms exploit their oligopsony power in the market
1Azar et al. (2017) document high levels of labor market concentration in US commuting zone and thathigher concentration reduces labor wages. Morlacco (2017) finds high buyer power of French firms in foreigninput markets. For a survey of the evidence of buyer power see Bhaskar et al. (2002).
1
for the specific input, by restricting their demand to pay a lower reward, in line with the
evidence of Azar et al. (2017). Moreover, firms exploit their oligopoly power in the market
for final goods, by restricting their supply to charge higher markups.
Our approach is based on the models of oligopoly of Atkeson and Burstein (2008) and
Edmond et al. (2015), which feature an inelastically supplied input (labor) in a perfectly
competitive market, as in the standard literature (Krugman, 1980; Melitz, 2003). In contrast,
we generalize several theories of firms’ market power in factors’ markets (Boal and Ransom,
1997; Bhaskar et al., 2002) by assuming an upward sloping supply curve for the input. A
few large firms demand the input and internalize their effects on the input’s reward. In line
with the evidence of Morlacco (2017), the oligopsony power of a firm depends on the firm’s
size in the market for the specific input: the larger a firm’s demand share is, the larger its
oligopsony power is. Larger oligopsony power reduces consumer’s welfare: by restricting the
demand for the specific input, firms restrict their output and charge higher markups. Thus,
our model features markups that are increasing both in the oligopoly power, as in Atkeson
and Burstein (2008), and in the oligopsony power.
We study the effects of international economic integration with two thought experiments,
which yield qualitatively similar results. First, we consider the exercise of Eckel and Neary
(2010) and model economic integration as an increase in the number of countries engaging
in frictionless trade. Second, we examine the effects of a symmetric reduction in iceberg
trade costs in a multi-country model. The effects of trade on oligopoly and oligopsony power
depend on which markets are affected by international economic integration.
Consider international integration in final goods markets while the input is only domes-
tically supplied. For this example, the input can be thought of as the labor supplied in
local labor markets. As in Edmond et al. (2015), trade in final goods has pro-competitive
effects: firms become smaller in the final goods market and their oligopoly power declines.
In contrast, the oligopsony power increases. In fact, the reduction in oligopoly power re-
duces profits and forces some firms to exit. Concentration in the final goods market declines
because the expansion of the final goods market offsets the reduction in the number of firms
from one country. However, the reduction in the number of firms increases market concen-
tration in the domestic input market and, thus, firms have higher oligopsony power. The
increase in oligopsony power dampens the pro-competitive effects of trade. The larger the
oligopsony power, the smaller the reduction in markups, and the smaller the increase in the
input’s reward. Although international economic integration brings about an increase in
welfare, the larger the oligopsony power of firms, the smaller the welfare gains from trade.
The effects of trade on firm’s market power are reversed in case of integration in the
market for the specific input. Consider firms that internationally source their input, and
2
only sell their final good domestically, which could represent the market of retailers. Free
trade of the input reduces the oligopsony power of firms, in line with the results of Morlacco
(2017). As firms from more countries purchase the same input, the demand share of each firm
in input markets decline, reducing firms’ oligopsony power. However, lower oligopsony power
causes a reduction in firm’s profits, which fosters firm’s exit. The decline in the number of
firms generates an increase in the oligopoly power of firms.
The presence of two sources of firms’ market power in two markets makes us reconsider
the effects of trade on firm’s market power. In fact, when firms are large both in final goods
markets and in inputs markets, the pro-competitive effects that arise by opening to trade
one market are dampened by the anti-competitive effects that originate in the other one.
Only economic integration in both markets reduces firm’s market power in each market.
Although the international trade literature has studied the role played by large oligopolists
(Atkeson and Burstein, 2008; Feenstra and Ma, 2007; Eckel and Neary, 2010; Amiti et al.,
2014; Edmond et al., 2015; Neary, 2016; Macedoni, 2017; Kikkawa et al., 2018), oligopsony
has received little attention. The early work of Bishop (1966), Feenstra (1980), Markusen
and Robson (1980), and McCulloch and Yellen (1980) studied the effects of a monopson-
istic industry in an otherwise standard Heckscher-Ohlin model. The authors find that the
presence of monopsony breaks down the Stolper-Samuelson theorem and that autarky may
yield higher welfare than trade. Some of the authors’ prediction are confirmed by our model
of oligopolists and oligopsonists producing differentiated goods: oligopsony generates distor-
tions in the market allocation, which are exacerbated by trade in final goods.
Our paper relates to studies that analyze sources of firm’s market power, other than
oligopoly and oligopsony. Raff and Schmitt (2009) consider the ability of retailers to exercise
market power by signing exclusive or non-exclusive contracts with manufacturers. Bernard
and Dhingra (2015) study the effects of exporters-importers contracts on welfare. Eckel and
Yeaple (2017) discuss the market power that large multiproduct firms have over workers
when they are able to invest in identifying workers’ skills. A feature of these papers, shared
by ours, is that trade, by increasing domestic market concentration, exacerbates market
distortions leading to ambiguous welfare effects.2 Finally, Morlacco (2017) estimates the
buyer power of French firms in foreign input markets.
The remainder of the paper is organized as follows. Section 2 builds a model of firms that
are both oligopolists and oligopsonists. Section 3 presents the effects of international trade
on firm’s market power. Section 4 provides our empirical results on the effects of market
2Markusen (1989) obtains an analogous result in a two-sector model in which an industry features thecostless assembly of differentiated inputs. Similarly, Arkolakis et al. (2015) showed that the distortionsoriginating from variable markups are exacerbated by trade.
3
power on prices. Section 5 concludes.
2 Model
Consider a static model of international trade. There are I countries indexed by i for origin,
and j for destination, and in each country there are Li consumers. To maintain tractability
in the presence of large firms, we follow the framework proposed by Eckel and Neary (2010):
there is a continuum of identical industries, and firms are large in an industry, but small
relative to the economy.
In each industry of country i, there is a discrete number Ni of firms, indexed by f .
We consider a model that only features homogeneous, large firms, which engage in trade of
differentiated varieties of a final good. The final goods market in each industry is oligopolistic.
Moreover, to produce the differentiated final good, each firm requires an input, whose total
supply in country i is denoted by Ki. The input is provided with an upward sloping supply
curve, and the market for the specific input is oligopsonistic. There is Cournot competition
both in the market for the input and in the market for final goods. Exporting a good from
i to j requires an iceberg trade cost τij, with τii = 1.
2.1 Consumer’s Problem
Consumers in country j = 1, ..., I have a two-tier utility function. The first tier is an additive
function of the utility attained by consuming the varieties produced across the z ∈ [0, 1]
industries:
Uj =
∫ 1
0
lnuj(z)dz (1)
Following Atkeson and Burstein (2008) and Edmond et al. (2015), we assume that uj(z) is
a Constant Elasticity of Substitution (CES) quantity index with elasticity of substitution
σ > 1:
uj(z) =
[∑i
∑f
qσ−1σ
fij
] σσ−1
(2)
where qfij is the quantity of the variety produced by firm f , exported from i to j, which
is sold at the price pfij. Consumers maximize utility (1) by choosing qfij, subject to the
following budget constraint: ∫ 1
0
∑i
∑f
pfijqfijdz ≤ yj (3)
4
where yj is the per capita income in j. The first order condition with respect to qfij yields:
λjpfij =q− 1σ
fij∑i
∑f q
σ−1σ
fij
where λj = y−1j is the marginal utility of income. A firm is large in its industry but, as there
is a continuum of industries, it is small relative to the economy. Hence, the firm does not
internalize its effects on λj and, therefore, we can normalize λj and yj to 1.
Letting xfij = Ljqfij denote the aggregate demand, the aggregate inverse demand is:
pfij =Ljx
− 1σ
fij∑i
∑f x
σ−1σ
fij
(4)
2.2 Supply of the Specific Input
To model oligopsony, we assume that the supply curve for the specific input Kj in country j is
upward sloping. Such an assumption generalizes several microfounded theories of oligopsony
(Boal and Ransom, 1997). To highlight the role of oligopsony power, and to maintain a
certain symmetry with the final goods market, we assume that the factor is supplied with
constant elasticity γ > 0. Let rj denote the price, or reward, for the input. The inverse
supply curve is given by:
rj = γ̃jKγj (5)
where γ̃j is a country specific supply shifter. In appendix 6.1.1, we outline an extension
to the baseline model in which workers experience disutility from supplying the input. In
contrast, the traditional literature in international trade dealing both with small (Krugman,
1980; Melitz, 2003) and large firms (Eckel and Neary, 2010; Edmond et al., 2015), assume
that the factors of production are inelastically supplied. If the specific factor is inelastically
supplied, which is equivalent to setting γ → ∞, firms would be able to reduce the input’s
price to zero.
Without loss of generality, let us assume that the input is supplied to domestic firms
only.3 Each firm f demands kfij units of the specific input to produce its differentiated
variety and sell it to country j. Firm f demand for the specific factor, denoted by kfi, is
given by summing kfij across the destinations the firm reaches, namely kfi =∑I
j=1 kfij.
Thus, aggregate demand for the specific input is∑Ni
f=1 kfi =∑Ni
f=1
∑Ij=1 kfij.
3If the input is internationally sourced, the aggregate demand would be given by∑Ii=1
∑Ij=1
∑Ni
f=1 kfij .
5
2.3 Firm’s Problem
Firms pay a fixed cost F , which is independent of the quantity produced and it is expressed
in units of the numeraire. The unit requirements to produce a variety xfij from i to j by
a firm f is τijcfij and is expressed in units of the oligopsonistic input. Hence, firm’s f
demand for the input is kfij = τijcfixfij. Let us re-write the inverse supply function of k
(5), to highlight the effect of a single firm on the reward for the input. By market clearing∑Ij=1
∑Nif=1 kfij = Ki, hence:
ri = γ̃iKγi = γ̃i
[I∑j=1
Ni∑f=1
τijcfixfij
]γ(6)
Firms maximize their profits by choosing xfij for each destination they serve, taking
other firms’ choices as given. Given the inverse demand function (4) and the inverse supply
function of the input (6), the profits of firm f equal:
πfi =∑j
pfijxfij − ri∑j
τijcfijxfij − F =
=∑j
Ljxσ−1σ
fij∑i
∑f x
σ−1σ
fij
− γ̃i
[∑f
∑j
τijcfixfij
]γ∑j
τijcfixfij − F = (7)
Firms are oligopolists in that they internalize their effects on the quantity index in the
demand function. Moreover, firms are oligopsonists: they internalize their effects on rj
through their demand of the specific input. Because of oligopsony power, the firm choice
of quantity in a destination j is not independent of the quantity choice in a destination j′.
Increasing the supply in j, increases factor’s price ri, and thus the marginal costs of the
quantity supplied across all destinations.
The first order condition with respect to quantity highlights the effects of market power
in the final good’s and the factor’s market:
σ − 1
σ
Ljx− 1σ
fij∑i
∑f x
σ−1σ
fij
1−xσ−1σ
fij∑i
∑f x
σ−1σ
fij︸ ︷︷ ︸Oligopoly Power
− riτijcfij1 + γ
∑j τijcfijxfij∑
f
∑j τijcfijxfij︸ ︷︷ ︸
oligopsony power
= 0 (8)
To provide intuition for the first order condition, we can represent both the extent of oligopoly
and oligopsony power by adequately defined revenue and demand shares. Let sfij denote the
6
oligopolist market share: the share of firm’s revenues over total revenues in a destination j.
Let sofi denote the oligopsonist demand share: the share of firm’s f demand for the input
over total demand in country i. The two market shares are defined as:
sfij =xσ−1σ
fij∑i
∑f x
σ−1σ
fij
(9)
sofi =kfi∑f kfi
=
∑j τijcfijxfij∑
f
∑j τijcfijxfij
(10)
By oligopoly power, the firm realizes that by increasing its supply of the good, it increases
the quantity aggregate and, thus, reduces the inverse demand function for all the goods in
the market. Such a reduction in demand has a larger effect on the firm, the larger its market
share sfij is. In addition, firms exhibit oligopsony power. By increasing the supply of a good,
the firm increases the demand for the factor of production, which results in an increase in
the factor’s price ri. The rise in ri increases the variable costs of production for all the
destinations the firm reaches. The effect of an increase in ri is proportional t the firm’s
demand share for the input sofi.
Using (9) and (10) into (8) yields the optimal quantity:
xfij =
Lj(σ − 1)
σ∑
i
∑f x
σ−1σ
fij
1− sfijτijcfijri(1 + γsofi)
σ (11)
Using (11) into (4) yields the pricing rule:
pfij = riτijcfijσ
σ − 1
(1 + γsofi1− sfij
)︸ ︷︷ ︸
Markup
(12)
As in standard models of oligopoly (Atkeson and Burstein, 2008; Edmond et al., 2015), firms
with higher oligopoly power — higher market share in the final goods market — enjoy higher
markups. Moreover, higher oligopsony power — higher market share in the input market —
increases markups as well. A firm with large sofi realizes that increasing its production raises
the price of the input. Therefore, larger values for sofi make firm f restricts its supply of the
final good by charging higher markups.
7
Firm’s revenues are given by:
pfijxfij =
[σ
(σ − 1)
τijcfijri(1 + γsofi)
1− sfij
]1−σ Lj∑i
∑f x
σ−1σ
fij
σ (13)
We can use the definition of market share xfij =sfijLjpfij
to derive the optimal quantity
supplied by a firm in a destination j, as a function of firm’s market power:
xfij =(σ − 1)Ljσriτijcfi
sfij(1− sfij)1 + γsofi
(14)
The larger the oligopsony power of a firm, the smaller its supply across all the destinations
reached. Moreover, there is a non-monotone, hump shaped relationship between supply of
the final good, and market share in a destination. When firms are small, a larger market
share is positively related to the supply of a good. When firms are large, namely their sales
account for more than half of the market, a larger market share reduces the total supply of
a good.
We exploit the definition of market share, xfij =sfijLjpfij
, to derive a simple expression for
firm’s profits as a function of oligopoly and oligopsony power. Profits in a destination j are
increasing both in oligopoly and oligopsony power:
πfij = xfijpfij − riτijcfijxfij = sfijLj − riτijcfijsfijLjpfij
=
= sfijLj
[1− σ − 1
σ
1− sfij1 + γsofi
](15)
Summing across the destinations reached yields firm’s total profits:
πfi =∑j
πfij − F =∑j
sfijLj
[1− σ − 1
σ
1− sfij1 + γsofi
]− F (16)
2.4 Market Clearing
Let us derive an expression for the total demand for Ki as well as its reward ri. The total
demand for the oligopsonistic input is the sum of individual demands for all firms in i.
8
Exploiting the definition of sofi (10), sfij (9), and the pricing rule (12), Ki becomes
Ki =
Ni∑v=1
kvi =kfisofi
=1
sofi
I∑j=1
cfijxfijτij =1
sofi
∑j
cfijτijLjsfijpfij
=σ − 1
σri
1
sofi(1 + γsofi)
∑j
Lj(1− sfij)sfij (17)
Combining the aggregate demand for the input (17) with the aggregate supply (5) yields the
equilibrium reward for the input:
ri =
[γ̃
1γ
i
σ − 1
σ
1
sofi(1 + γsofi)
∑j
Lj(1− sfij)sfij
] γ1+γ
(18)
The final goods market clearing condition is given by:
I∑i=1
Ni∑f=1
sfij = 1
Similarly, the sum of the oligopsonistic market shares equal one:
Ni∑f=1
sofi = 1
Finally, let us derive the equilibrium level of the CES quantity index Qj as a function of
domestic variables. By using the definition of aggregate quantity, we obtain∑
i
∑f x
σ−1σ
fij =
(QjLj)σ−1σ . Consider the revenues for a firm from j to j, defined in (13). Since revenues
pfjjxfjj = sfjjLj, and the quantity aggregator∑
i
∑f x
σ−1σ
fij = (QjLj)σ−1σ , the CES quantity
index can be expressed as a function of the domestic reward for the input rj, and the market
share of the domestic firm in the domestic final goods market and input market:
Qj =σ − 1
στjjcfjrj
(1− sfjj)s− 1σ−1
fjj
1 + γsofj(19)
Consistent with the findings of Edmond et al. (2015), larger oligopoly power, all else constant,
reduces the welfare of consumers. Moreover, oligopsony power has a similar effect: larger
oligopsony power reduces welfare.
9
3 The Effects of International Trade
We consider firms that are homogeneous in terms of productivity: cfi = ci ∀ f = 1, ..., Ni.
The equilibrium is a vector of the number of firms in each country Ni and specific factor
price ri, such that each firm chooses the optimal quantity xij according to (11), profits (16)
equal zero, final goods market clear, factor’s market clear and trade is balanced. To gather
some intuition on the effects of international trade on the oligopsonist and oligopoly power
of firms, let us consider a version of the baseline model with I identical countries. Let N
denote the number of firms in each country, and L each country size.
What are the effects of international trade on firm’s market power? To answer to this
question we consider two thought experiments. First, we replicate the Eckel and Neary (2010)
exercise in our framework: we study the effects of an increase in the number of countries
that engage in frictionless trade of final goods or inputs. Second, we study the effects of a
reduction in iceberg trade costs in a multi-country setting.
3.1 International Economic Integration
In this section, we study the effects of international economic integration modeled, as in Eckel
and Neary (2010), as an increase in the number of countries in the context of frictionless
trade, namely all iceberg trade costs τij are equal to one. Let I denote the number of countries
with integrated final goods markets, and Io the number of countries with integrated input
markets. Since all firms are identical, and there are no iceberg trade costs of exporting, the
market share of a firm in the final goods market of any country is given by s = 1IN
, while
the demand share of each firm for the input is so = 1IoN
. Adapting the zero profit condition
(16) to the symmetric countries assumption yields:
IsL
[1− σ − 1
σ
1− s1 + γso
]= F (20)
To understand how international economic integration affects the market power in the
final goods and input markets, we consider two equilibrium conditions. The first one repre-
sents the relative market power (RMP) of firms in the final goods markets as a function of
the number of integrated countries:
s
so=Io
I(RMP)
The relative market power of firms sso
is inversely related to the relative number of integrated
countries Io
I. All else constant, the larger the number of integrated countries in the final goods
10
market is, the smaller the market share in the final goods market is. In the plane (s, so),
RMP represents a linear relationship between s and so, whose slope depends on the relative
number of integrated countries for the two markets. The positive slope represents the fact
that an increase in the size of a firm, all else constant, increases the firm’s market power in
both markets.
The second equation is the zero profit condition (20):
so =σ − 1
σγ
1− s1− F
IsL
− 1
γ(ZP1)
s = 1− σ
σ − 1
[1 + γso − F
IosoL− F
IoL
](ZP2)
where ZP1, is the zero profit condition (20) rearranged and ZP2 is obtained by substituting
I = Iosos−1 using RMP. In the plane (s, so), the zero profit condition is represented by
a negative relationship between s and so. All else constant, to maintain profit constantly
at zero, an increase in firm’s market power in a market has to be matched by a reduction
in market power in the other market. Armed with RMP and, depending on which is more
convenient, ZP1 and ZP2, we can now study the effects of international economic integration.
Let us start considering the effects of integration in the final goods market. As figure
1 shows, if the number of countries I that engage in trade of the final goods increases, the
market share s declines, while the demand share so for the input increases. Integration of
final goods market increases the competition faced by oligopolists, who lose market share s.
As the number of firms active in the final goods market increases, each of them have a smaller
share. Economic integration generates the pro-competitive gains illustrated by Edmond et al.
(2015). However, by the zero profit condition, the reduction in the market share causes some
firms to exit. The exit of firms increases the concentration in the oligopolistic input market.
As a result, the demand share so increases. While integration of final goods market reduces
the oligopoly power, it has an opposite effect on the oligopsony power, which increases.
Integration of the input market has the opposite effect. Figure 2 illustrates that an
increase in the number of countries with integrated input markets Io causes the market
share s to increase, and the demand share for the input so to decline. As the number of
firms in the market for the input increases, the demand share of each firm declines. The
decline in so reduces the profitability of firms and, by the zero profit condition, some firms
exit. As a result, fewer firms are serving the final goods market, which increases the market
share s.
When firms are large both in the destination and in the market for factors of production,
the pro-competitive effects that arise from opening to trade one of the two markets are
11
Figure 1: Final Goods Market Integration Figure 2: Input Market Integration
dampened by the anti-competitive effects in the other. Opening trade for final goods reduces
the market power of firms in the destination, but since the number of firms in each country
falls, the oligopsony power increases. On the other hand, free trade in inputs reduces the
oligopsony power, but it increases the market share of firms in their domestic economy. Only
economic integration in all markets reduces the market power of firms both in the market
for final goods and in the market for inputs. Figure (3) illustrates the effects of an increase
in the number of integrated countries I = Io. As firms lose market power in both market,
both so and s decline.
Figure 3: Final Goods and Input Market Integration
=
12
3.1.1 Input Price, Markups and Welfare
This section summarizes how oligopsony power affects input prices, markups and welfare in
the presence of an increase in the number of countries with integrated final goods markets.
The derivations are in appendix 6.1.2.
International economic integration increases the reward for the input: despite the in-
crease in market concentration, increasing I leads to higher r. The larger the oligopsony
power of firms, the smaller the increase in the input’s compensation following international
economic integration. When firms have only oligopoly power, economic integration leads to
higher production, which increases the input demand and, thus, reward. In the presence of
oligopsony power, the rise in input market concentration dampens the gains for the input,
without completely offsetting them.
An increase in the number of countries with integrated final goods markets has a twofold
effect on markups. On the one hand, a reduction in market share brings down markups. On
the other, the increase in oligopsony market power has a positive effect on markups. The first
effect dominates, and economic integration reduces the markups of firms. However, the larger
the oligopsony power of firms, the smaller the reduction in markups. The pro-competitive
gains from trade are dampened by the concentration in the input market.
Finally, an increase in the number of countries with integrated final goods markets in-
creases consumer’s welfare. However, the larger the oligopsony power of firms, the smaller
the gains. Too see this, let us consider the total (log) change of the CES quantity index —
which is equivalent to the change in welfare — as a function of the change in the oligopoly
and oligopsony power:
d lnQ =
[1
σ − 1+
s
(1− s)(1 + γ)
](−d ln s) +
[γso
(1 + γso)(1 + γ)
](−d ln so) (21)
The change in welfare is similar to the welfare formula developed by Macedoni (2017). The
change in welfare is a function of the change in the oligopoly (d ln s) and oligopsony (d ln so)
power of firms, and on the current level of oligopoly (s) and oligopsony (so) power. In
particular, a reduction in the two sources of market power, generates welfare gains. Moreover,
larger initial levels of market power magnify the effects of a change in market share.
3.2 Effects of a Reduction in Trade Costs
In this section, we study the effects of international economic integration modeled as a
reduction in the iceberg trade costs. We keep the assumption of I symmetric countries, and
13
assume that the input is domestically sourced.4 Let τij = τji = τ for i 6= j and τii = 1, ci = c
and Li = L for ∀i ∈ {1, ...I}. As in the previous section, due to symmetry, Ni = N and
ri = r. We leave the detailed derivations to appendix 6.1.3.
To simplify the notation, let the market share in the final goods market be s = sjj in
the domestic economy, and s∗ = sij = sji in export markets. As the input is domestically
sourced, the oligopsonist share is the reciprocal of the number of firms from one country:
so = 1N
. The domestic and export market share in final goods are linked by the following
relationship:
s1
σ−1
1− s= τ
s∗1
σ−1
1− s∗
For τ > 1, the domestic market share is always larger than the export market share. Hence,
export markups are lower than domestic markups.
The RMP curve, which reflects the relative domestic market power of oligopolists and
oligopsonists, is represented by the following expression:
1− ss
1σ−1
=1
τ
1− so−sI−1(
so−sI−1
) 1σ−1
(RMP)
Appendix 6.1.3 proves that the RMP curve is represented by an increasing function in the
(s, so) plane, similarly to the RMP curve of the previous section. A reduction in the iceberg
trade costs for final goods, rotates the RMP curve clockwise. Lower iceberg trade costs
increases the competition faced by firms in the domestic final goods market. Hence, holding
the oligopsony power constant, lower iceberg trade costs reduce the market power in domestic
final goods markets.
In the presence of symmetric countries and iceberg trade costs, firm’s profits are the sum
of the profits obtained in the home country and the profits obtain in export markets. The
zero profit (ZP) condition, becomes:
ZP (s, so) ≡ so +σ − 1
σ
1
1 + γso
[s
I − 1(Is− 2so)
]− σ − 1
σ
1
1 + γso
(so − 1
I − 1(so)2
)=F
L
The right-hand side of the ZP condition consists of three component. The first term, so = 1N
,
represents the direct effect of firm’s entry on an individual firm’s revenues. The second term,
reflects the impact of trade costs on entry decisions. In fact, changes in trade costs affect
entry by varying the domestic and export market shares of firms. Finally, the third term
reflects the indirect effect of competition: smaller iceberg trade costs make foreign rivals
4In the appendix, we outline a model in which firms internationally source a set of differentiated inputs,and imports of inputs are subject to iceberg trade costs.
14
more competitive, reducing domestic profits and entry.
By the implicit function theorem:
ds
dso= −dZP/ds
o
dZP/ds< 0 (22)
Hence, the ZP curve is decreasing in the (s, so) plane, analogously to the previous section.
Holding the profits equal to zero, higher market power in domestic final goods markets has
to be met by a reduction in market power in the domestic input.
The effects of a reduction in iceberg trade costs can be studied by use of a graph similar
to figure 1. A reduction in trade costs rotates the RMP curve clockwise. Thus, the new
equilibrium features higher oligopsonistic market share so and lower oligopolistic domestic
market share s. A reduction in trade costs generates similar predictions of an increase in the
number of integrated countries we explored in the previous section. Lowering iceberg trade
costs reduces the domestic oligopoly power in final goods, but it increases the oligopsony
power.
Lower trade costs increase export revenues while reducing domestic sales. Thus, the
oligopoly power in export markets increases while the domestic oligopoly power declines.
The shift in oligopoly power forces firms to reallocate their resources from the domestic,
high-markup production, to the export, low-markup production. As a result, firm’s profits
decline forcing some firms to exit. As fewer firms are demanding the domestic input, the
oligopsony power increases.
The effects of a reduction in iceberg trade costs on input prices are similar to the experi-
ment of increasing the number of integrated countries. Lower trade costs rise the input price,
however, the larger the oligopsony power, the lower the increase in input price. Moreover,
the welfare formula in (28) is also valid for a world with iceberg trade costs.
4 Test of the Predictions of the Model
This section tests the prediction of the model on the pricing behavior of firms. From (12),
the price a firm charges in a destination is a function of the marginal costs of production and
delivery, of the demand share of the firm in inputs’ markets, and of the market share of the
firm in the destination. While the effects of oligopoly power in the market for final goods on
prices have been extensively studied and documented (Atkeson and Burstein, 2008; Edmond
et al., 2015; Hottman et al., 2016), our empirical contribution is to show that oligopsony
power is also a quantitatively relevant source of market power that influences prices.
15
4.1 From the Model to the Data
To connect the theory to the data, let us consider the pricing decision of a firm f from
country i exporting to country j in industry k. We assume that inputs are domestically
sourced. Since our data covers multiple years, we also add a time subscript t. We consider
the following approximation of the total derivative of log prices (12):
d ln pijkft = d ln(cijftτijtrikt) + d ln(1 + γdsoikft
)− d ln (1− sijkft)
≈ d ln(cijftτijtrikt) + γdsoikft + dsijkft (23)
As we describe in the following section, our data comprises of highly disaggregated industry-
level prices. Thus, we consider the industry average of (23):
d ln p̄ijkt ≈ d ln c̄ijkt + γds̄oikft + ds̄ijk
where p̄ijkt =∑Nijktf pijkft
Nijkts̄oikt =
∑Njktf soikftNikt
and s̄ijkt =∑Njktf sijkft
Njktare the average indus-
try price, demand share in inputs’ markets, and market share in the destination. Finally,
c̄ijkt =∑Nijktf cijftτijtrikt
Nijktis the industry average marginal cost of production and delivery,
which reflects firms’ productivity, iceberg trade costs, and input prices.
As data on average market shares of firms across destination is hard to gather, we consider
alternative measures of market concentration to proxy for the average market share in inputs’
and final goods’ markets. In particular, we proxy the average demand share in inputs’ market
s̄oikt with the corresponding origin and industry specific Herfindahl Index HIoik. Moreover,
we proxy the average market share s̄ijkt with the corresponding country pair and industry
specific Herfindahl Index HIdijk. Although using Herfindahl Indexes (HI) to proxy for average
market share may reduce the precision of our estimates, we should note that the average
market share equals the HI in case of symmetric firms.5
Finally, we assume that the average marginal cost of production and delivery can be
decomposed in an industry-year component ξkt that reflects industry-specific shocks, and a
country-pair-year component θijt that controls for input prices, productivity levels, and for
bilateral trade costs. Namely, we let ln c̄ijkt = ξkt + θijt
Thus, the regression model we use to estimate the effects of oligopoly and oligopsony
5We can relax this assumption: for a given distribution of firms’ sizes there exists a mapping betweenaverage market share and Herfindahl index. Besides, even in the asymmetric case for a given distribution offirms’ sizes, higher Herfindahl indexes will be associated with higher firms’ average market share.
16
power on prices is the following:
ln p̄ijkt = γHIoikt + βHIdijkt + ξkt + θijt + εijkt (24)
where the three components of the average marginal cost of production and delivery are
estimated via fixed effects, and εijkt is the error term. We refer to HIoikt as the origin HI,
which proxies oligopsony power, and to HIdijkt as the destination HI, which proxies oligopoly
power.
A possible concern that arises when using unit prices is the heterogeneity in product
quality across industries and destinations. Our use of fixed effects absorbs quality related
variation if those can be decomposed by exporer-, importer-, industry-, and country pair-
specific components. The country-pair fixed effect addresses the ”Washington apples” effect,
whereby higher quality goods are shipped over longer distances. Similarly, quality differ-
ences due to destinations’ level of development and tastes are captured by country-pair and
industry-year fixed effects.
Our main empirical result is to document a positive relationship between oligopsony
power and prices. We also confirm the results from the literature that prices increase in
oligopoly power in the destination market. However, both the statistical and economic
significance of our results suggest that oligopsony power has a larger quantitative effect than
oligopoly power.
4.2 Data
To estimate (24), we collect data from three sources. First, we use data on unit prices from
international trade data. Second, we collect data on HI for each country i and industry
k. Finally, we gather data on input-output tables to conduct robustness exercises on the
definition of market concentration. Let us now describe the three data sources in detail.
Unit prices
We use data on bilateral trade flows from the World Bank’s WITS database. The data
contain information on physical quantities, which allows us to obtain unit prices p̄ijkt for
each country pair ij, industry k and year t. An industry k is a Harmonized system (HS)
four-digit code. The dataset covers 170 countries and is available for the years 1988-2013.
17
Herfindahl Indexes
As a measure of market concentration we use Herfindahl indexes (HI) computed by Feenstra
and Weinstein (2017) on a country-industry level. Using our notation, these HI are denoted
by HIik. Depending on the country and industry, HIik is constructed using the shares of
total shipments or total sales of firms from i in industry k. Thus, HIik captures the level
of market concentration that prevails across firms from the same country and industry. We
use this measure of concentration as a proxy for oligopsony power. HIik exactly measure
concentration in domestic input markets if all firms use the same set of domestic inputs and
in the same proportions.
Feenstra and Weinstein (2017) use several sources to construct HIik across countries. For
the United States, the authors use the data provided by the US Census of Manufacturers. As
the Census classifies industries at the NAICS six-digit level, and the unit price data is at the
HS four-digit code, there is a concordance issue when there is more than one HS four-digit
industry per NAICS industry. In such cases, the authors assume the same Herfindahl Index
for each HS four-digit code within a NAICS six-digit code.
Feenstra and Weinstein (2017) obtain Herfindahl Indexes for Mexico from Encuesta In-
dustrial Anual (Annual Industrial Survey) of the Instituto Nacional de Estadistica y Ge-
ografia. The dataset covers 205 CMAP94 categories and 232 HS four-digit industries for
1993 and 2003. For Canada, the authors purchased market concentration measures for 1996
and 2005 from Statistics Canada.
For the rest of the countries, the authors use PIERS data on firm-level shipments to the
US in 1992 and 2005. PIERS data provide information on sea shipments to the US of the
50,000 largest exporters. Feenstra and Weinstein (2017) assume that market concentration
does not depend on the mode of transportation and adjust HIs with a fraction of sea ship-
ments in total trade volume on country-industry level. Details are available in the appendix
of Feenstra and Weinstein (2017).
Since the HIs from different sources have different coverage, Feenstra and Weinstein
(2017) choose 1992 and 2005 as the benchmark years as most of the data is available for
these years. They linearly extrapolate their data based on years available for Mexico and
Canada to construct HIs for 1992 and 2005.
Due to data availability, merging the dataset on unit prices with the dataset on HIs,
limits us to consider 117 countries for the years 1992 and 2005. The number of HS four-digit
industries is 1198.
18
Input-Output Tables
In order to construct alternative measures of market concentration in inputs’ market, we
additionally use the Eora Multi-Region Input-Output database. This database provides
information on input-output linkages between 26 sectors across 181 countries. Since measures
of concentration we have are available for traded goods only, so we consider 11 tradable
sectors in Eora database. We abstract from physical input requirements and normalize the
Input-Output tables so that they provide shares for input requirements from all industries
for each country and industry.
In order to merge Input-Output tables with the other two datasets, we first use the
concordance between HS four-digit codes and SITC rev. 3 two-digit codes.6 Then, we use
the crosswalk between SITC and Eora classification from Feenstra and Sasahara (2017).
4.2.1 Summary Statistics
Figure 4 shows the distribution of HIs in the US in 1992 and 2005 across industries. There is
significant market concentration, which, according to our model, will be reflected in domestic
input markets. To understand the magnitude of HIs, suppose all firms within an industry
are identical. An HI of 0.2 corresponds to an average market share of 20%. Such a result
is consistent with the findings of Azar et al. (2017) in the US labor market, and Morlacco
(2017) in French imported inputs markets.
The distribution additionally highlights significant heterogeneity across industries, with
the larger mass of industries around values below 0.2. A smaller number of industries register
larger levels of market concentration, with HIs larger that 0.5.
Figure 4: Distribution of US HIs across industries
1992
0.0
5.1
.15
.2Fr
actio
n
0 .2 .4 .6 .8 1(mean) HI
2005
0.0
5.1
.15
Frac
tion
0 .2 .4 .6 .8 1(mean) HI
Figure 5 shows the distribution of weighted average HIs across all the countries in the
6https://unstats.un.org/unsd/trade/classifications/correspondence-tables.asp
19
sample, where weights are squared import share of each industry in total imports for each
country. As a consequence of the aggregation, the levels of concentration decline. However,
the figure highlights significant cross-country heterogeneity, with average HIs ranging from
0 to 0.5.
Figure 5: Distribution of weighted average HIs across countries
1992
0.2
.4.6
.8Fraction
0 .1 .2 .3 .4 .5tHI
2005
0.2
.4.6
.8Fraction
0 .2 .4 .6tHI
The weigthed average HIs exactly equals the economy-wide concentration in case there are
no firms producing in multiple HS four-digit industries. Since the literature has extensively
documented the relevance of multiproduct firms (Bernard et al., 2011), the weighted average
of industry HIs underestimates aggregate concentration. To limit the bias, we consider the
distribution of the median industry HI across countries in Figure 6.
The figure shows a staggering level of concentration. The distribution shows that in
more than 50% of countries the median industry for HI has a level of market concentration
equivalent to that of a duopoly with two identical firms (0.5). Such a level of concentration
among domestic firms, according to our model, has large effects on prices. In the next
section, we test such a prediction.
Figure 6: Distribution of median world HIs
Figure 7: 1992
0.2
.4.6
.81
Fraction
.1 .2 .3 .4 .5medHI
Figure 8: 2005
0.1
.2.3
Fraction
0 .2 .4 .6 .8 1medHI
20
4.3 Results
Using the data described, we estimate (24) by OLS. We consider several specifications and
table 1 presents the results.
Our baseline specification considers the relationship between our measures of market
concentration and the unit prices for all country pairs in our sample. In the baseline spec-
ification, we let the measure of oligopsony power, or origin HI, HIoikt = HIikt. Moreover,
we assume that the measure of oligopoly power in the destination, or destination HI, is
HIdijkt = HIjkt, and, thus, is only a function of the destination characteristics.
The first column of table 1 shows that both measures of market concentration, which
proxy for market power, have positive and statistically significant coefficients. An increase
in the origin HI by one standard deviation is associated with an increase in average industry
prices by 3.7%. On the other hand, an increase in destination HI by one standard devia-
tion generates an increase in industry price of 0.8%. The results are, thus, consistent with
the prediction of our models. In the following paragraphs, we conduct further robustness
exercises, considering alternative model specification and measures for our variables.
Alternative Destination Concentration Measure
In our baseline specification, the origin and destination HI are symmetric. Namely, the HI
of the US proxies the market concentration in US input’s market and the concentration of
all exporters in the US final goods market. A possible concern is that the destination HI not
only captures market concentration, but also the market power of firms in the destination
country, which would underestimate the effects of oligopoly power. To mitigate such concern,
we consider an alternative measure of the concentration in the final goods market, keeping
the baseline definition for origin HI.
We follow Feenstra and Romalis (2014) and consider HIdijkt = HIiktλijk, where λijk is
the trade share of country i over total imports to j in industry k. To exactly measure trade
shares we need domestic absorption as denominator. Due to lack of data, we consider as
denominator the total values of imports to j. Country-pair-year fixed effects capture the
heterogeneity across countries of ratio of total imports to domestic absorption, and hence
allow to address this measurement error.
Results are in column 2 of table 1. The coefficient on the origin HI, which proxies
oligopsony power, is barely affected. The coefficient on the destination HI, which proxies
oligopoly power, is larger than baseline but insignificant.
21
Table 1: The Effects of Oligopsony and Oligopoly Power on Prices
Baseline Adj Dest HI US Origin Adj Origin HI Adj Origin/Dest HIOrigin HI 0.150*** 0.148*** 0.524*** 0.558*** 0.558***
(0.006) (0.006) (0.096) (0.084) (0.085)Destination HI 0.030*** 0.275 -0.008 0.027*** 0.181
(0.006) (0.906) (0.022) (0.006) (0.770)Industry-Year Y Y N Y YCountry-Pair-Year Y Y N Y YDestination N N Y N NIndustry N N Y N NYear N N Y N NR2 0.69 0.69 0.88 0.69 0.69# Observations 883280 883280 36859 858898 858898
Robust standard errors are in the parentheses. Baseline: HIs from Feenstra and Weinstein (2017) fororigin and destination countries as dependent variables. Adj Dest HI: alternative measure of concen-tration in the destination market. US Origin: only data on US export unit values. Adj Origin HI:alternative measure of concentration in the origin market. Adj Origin/Dest HI: alternative measures ofconcentration in origin and destination market. Details in the main text.
United States as the only origin
US data on market concentration comes straight from the Census of Manufacturers, and
is more reliable than HIs in other countries constructed from US import data. In order to
check if our results hold on a smaller subsample of more reliable data, we consider only unit
prices from the US to the destination countries. As there is only one exporting country, we
cannot use country-pair-year fixed effects, so for this robustness check we include destination,
industry and year fixed effects. We use the baseline definitions for origin and destination HI.
The result are in column 3 of table 1. The coefficient on origin HI is positive and
significant, and is larger than in other specifications. An increase by one standard deviation
in the origin HI increases prices by 10%. Due to significantly lower number of observations,
and destination fixed effects, the coefficient at destination HI is not significant.
Constructing Alternative Origin Concentration Measure
In the baseline specification, we assumed that each industry uses its own specific factor. In
this section, we relax this assumption and assume that firms from different industries can
use the same factors of production. As a result, one firm’s oligopsony power depends on
its input requirements and on the relative size of the firm’s industry demand in the input
industries. We employ detailed input-output data to construct measures of concentration in
line with this logic.
22
As input-output data is on the higher level of aggregation than trade data, we start with
constructing aggregate HIs. We construct the HI for each of the k = 1, ..., 11 Eora manufac-
turing industries in every country i, HIEoraik , as the weighted sum of HIs of corresponding HS
four-digit industries HIHS4iv , where industry v belongs to the Eora industry k. The weigths
are the squared shares of each HS four-digit industry’s output in the output of Eora industry
siv. In particular, we compute HIEoraik as
HIEoraik =∑v∈k
HIHS4iv s2iv
where we dropped the time subscript for the sake of exposition. For each industry k in
country i, we compute their demand share on each factor’s market m as:
shareimk =ximIOimk∑m ximIOimk
where IOimk is an input share from industry m to industry k, and xim is a total output of
industry m in country i.7
Multiplying industry k HI (HIEoraik ) by the demand share of industry k for inputs from
industry m (IOimk) yields a proxy for the oligopsony power of firms from industry k in the
input market m. To obtain an aggregate measure of market concentration over the inputs
purchased by firms in industry k, we take the weigthed sum of HIEoraik shareimk, where the
weights are each industry are the squared demand shares of industry k in each market m
(shareimk). As a result, we obtain the following adjusted measure of HI for the inputs used
by industry k:
HIadjik =∑m
HIEoraik IOimkshare2imk
HIadjik has two attractive properties: first, it reflects the fact that smaller industries using
common factor are going to have lower oligopsony power. Second, industries that are using
specific factors intensively are going to have higher oligopsony power.8 In column 4 of table 1,
we consider HIoikt = HIadjikt and use the baseline measure for HIdijkt. Results are qualitatively
similar to the baseline specification, suggesting that our results in the previous section are
not driven by the assumptions on the structure of inputs market. In this case, a one standard
deviation increase in origin HI is associated with a 0.95% increase in prices, in destination
HI with a 0.5% increase in prices.
Finally, adopting the adjusted measures of origin HI and destination HI in the same
7We find total output from volume of imports importsik and domestic share λiik: xik = importiik1−λiik
λiik.
8The theoretical assumptions behind the adjusted measure of origin HI are outlined in the appendix.
23
specification yields similar results to our baseline case. The result of this specification are in
column 5 of table 1.
5 Conclusions
The literature in international trade has explored the consequences of the presence of large
exporters, which exploit their oligopoly power, on firms’ prices and scope as well as on
the welfare of consumers (Eckel and Neary, 2010; Edmond et al., 2015). In this paper, we
have argued that firms’ market power in the market for inputs, in which firms exploit their
oligopsony power, has major implications for prices and welfare.
Using data on market concentration from Feenstra and Weinstein (2017), we documented
that concentration in the market for inputs is associated with higher prices and lower export
volumes. Moreover, concentration in the input market, which is a proxy for oligopsony
power, has economically larger effects than concentration in the final goods markets.
Our theoretical model shows that while international integration in the market for final
goods reduces firms’ market power in the final goods market, it has the opposite effect on the
market power of firms in input markets. The pro-competitive gains arising from international
competition between oligopolists are dampened by the anti-competitive effects of increase in
market concentration in the market for inputs. Only international integration in both final
goods and input markets successfully reduces firms’ market power.
The policy implication is straightforward: to maximize the welfare gains from trade,
trade agreements should foster trade both in final goods markets and in input markets. In
the presence of domestic inputs, policies that reduce market concentration for domestic input
could reduce the anti-competitive effects of trade in final goods.
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6 Appendix
6.1 Theory
This section provides the details of our theoretical results, and outlines the extensions toour baseline model mentioned in the main text. First, we show how the supply curve for theoligopsonistic factor can be microfounded by adding labor-disutility to consumers’ utility.Second, we show how we derive the results on the effects of international integration oninput prices, markups, and welfare. Third, we derive the RM and ZP curves in a model withiceberg trade costs. Fourth, we show how our model predictions in terms of prices generalizeto a model where firms purchase multiple inputs. Finally, we describe how the definition ofoligopsony power changes when firms from multiple industries demand the same input.
26
6.1.1 Endogenous Supply of the Input
Consider the following utility function, that allows us to endogenize the upward slopingnature of the supply for the input. Consumers in country j = 1, ..., I have the followingCobb-Douglas aggregation of the CES quantity index Qj we use in the baseline model, andthe disutility from supplying the input kcj , which is denoted by Hj:
uj = QαjH
1−αj
We assume an exponential disutility from supplying kcj :
Hj = exp(−(kcj)1+γ)
Consumers’ per capita income is denoted by yj = wj + rjkcj , where wj is the labor wage and
rj represents the payments to the input kcj . Consumers maximize utility by choosing qfijand kc, subject to the following budget constraint:∑
i
∑f
pfijqfij ≤ wj + rjkcj
Solving the consumer’s problem yields the following inverse demand function for the varietyproduced by firm f from i to j
pfijyj
=q− 1σ
fij
Qσ−1σ
j
=q− 1σ
fij∑i
∑f q
σ−1σ
fij
and the individual inverse supply of the input:
rjyj
=(1− α)(1 + γ)
α(kcj)
γ
Let xfij = Ljqfij denote the aggregate demand and Kj = Ljkcj denote aggregate supply of
the input. Aggregate inverse demand and supply are given by:
pfijyj
=Ljx
− 1σ
fij∑i
∑f x
σ−1σ
fij
rjyj
= γ̃jKγj
where γ̃j = (1−α)(1+γ)αLγj
. Taking per capita income as the numeraire, and thus normalizing yj
to one, yields the same expressions we use in the baseline model.
6.1.2 International Integration
This section derives the effects of international economic integration on input prices, markupsand welfare stated in section 3.1. Let us start with input prices. Re-writing (18) in the
27
symmetric country case yields:
r =
[γ̃
1γσ − 1
σ
IL(1− s)sso(1 + γso)
] γ1+γ
(25)
All else constant, increases in the market power of firms — either in the final goods orinput markets — reduces the demand for the input, and hence its compensation. On theother hand, the larger the number of countries with integrated input markets, the larger thecompensation of the input. Let us fix Io = 1 and consider the effects of integration in thefinal goods markets. Using the zero profit condition, we can rewrite the compensation forthe input as:
r =
[γ̃
1γ
(L− F
so
)] γ1+γ
The compensation for the input negatively depends on the demand share of firms for suchan input. International economic integration increases the reward for the input: despite theincrease in market concentration, increasing I leads to higher r:
d ln r
d ln I=
γ
1 + γ
F
Lso − Fd ln so
d ln I(26)
To understand how the oligopsony power of firms influences factor’s compensation, let us andconsider the elasticity of the oligopsonist demand share relative to the number of countries:
d ln so
d ln I=
(σ − 1)s
σ(1 + γso)− (σ−1)(1−2s−γsso)1+γso
(27)
The elasticity of the oligopsony power with respect to the number of countries with inte-grated final goods’ markets is declining in so. The larger the oligopsony power, the smallerthe increase in the oligopsony power following an increase in the number of countries. Thus,the larger the oligopsony power of firms, the smaller the increase in the input’s compensationfollowing international economic integration. When firms have only oligopoly power, eco-nomic integration leads to higher production, which increases the input demand and, thus,reward. In the presence of oligopsony power, the rise in input market concentration dampensthe gains for the input, without completely offsetting them.
An increase in the number of countries with integrated final goods markets has a twofoldeffect on markups. On the one hand, a reduction in market share brings down markups. Onthe other, the increase in oligopsony market power has a positive effect on markups. Thefirst effect dominates, and economic integration reduces the markups of firms:
d lnµ
d ln I=
s+ γso
(1− s)(1 + γso)
d ln so
d ln I− s
1− s=
= − s
1− s
[1 + (σ − 1)s+ σγso
σ(1 + γso)− (σ−1)(1−2s−γsso)1+γso
]
What is the effect of oligopsony power on the markup elasticity? On the one hand, for a
28
given change in the number of firms, larger oligopsony power generates smaller reduction inmarkups following integration. On the other hand, larger oligopsony power generates smallerchanges in the number of firms, which then generates smaller changes in markups. The firsteffect dominates, as the markup elasticity is, in absolute value, increasing in so. The largerthe oligopsony power of firms, the smaller the reduction in markups. The pro-competitivegains from trade are dampened by the concentration in the input market.
Let us now consider the effects of international economic integration in final goods mar-kets on the welfare of consumers, by examining the CES quantity index Q:
Q = c−1[σ − 1
σγ̃
] 11+γ s−
1σ−1 (1− s)
11+γ
(1 + γso)1
1+γ
(28)
The total (log) change of the CES quantity index — which is equivalent to the change inwelfare — is a function of the change in the oligopoly and oligopsony power:
d lnQ =
[1
σ − 1+
s
(1− s)(1 + γ)
](−d ln s) +
[γso
(1 + γso)(1 + γ)
](−d ln so) (29)
The change in welfare is similar to the welfare formula developed by Macedoni (2017). Thechange in welfare is a function of the change in the oligopoly and oligopsony power of firms,and on the current level of oligopoly and oligopsony power. In particular, a reduction inthe two sources of market power, generates welfare gains. Moreover, larger initial levels ofmarket power magnify the effects of a change in market share.
An increase in I has a twofold effect on welfare. On the one hand, by reducing the marketshare of in the final goods markets (−d ln s > 0), economic integration improves welfare. Onthe other hand, by increasing the demand share of firms in the input market (−d ln so < 0),it reduces it. To verify the total effect, it is convenient to rewrite (28) using the the zeroprofit condition 1−s
1+γso= σ
σ−1
[1− F
Lso
].
Q = c−1[
α(σ − 1)
σ(1− α)(1 + γ)
] 11+γ
s−1
σ−1
[1− F
Lso
] 11+γ
Using such an expression, the total change in welfare is given by:
d lnQ = − 1
σ − 1d ln s+
F
(1 + γ)(Lso − F )d ln so
Thus, the total effect of an increase in the number of countries with integrated final goodsmarkets is positive: welfare increases. The larger the oligopsony power of firms, the smallerthe gains.
6.1.3 Iceberg Trade Costs
This section presents the detailed derivations of the model discussed in section 3.2. Recallthe assumption of symmetric countries, and that so = 1/N . First, we derive the RMP curvethat reflects the relationship between oligopoly and oligopsony power in the domestic market.
29
Let an asterisk denote variables associated with exports. Since all firms are identical, allfirms also export to all I − 1 destinations different from the domestic country. Moreover, asall countries are identical, export quantities and prices are identical across destination.
Using the definition of oligopolist market share, the domestic market share in final goodsmarket equals
s =xσ−1σ
jj∑iNix
σ−1σ
ij
=xσ−1σ
Nxσ−1σ + (I − 1)Nx∗
σ−1σ
= so(xx∗
)σ−1σ(
xx∗
)σ−1σ + (I − 1)
(30)
Similarly, export oligopoly power equals
s∗ = so1(
xx∗
)σ−1σ + (I − 1)
Thus, the ratio of domestic market share to export market share equals
s
s∗=( xx∗
)σ−1σ
(31)
Using the pricing rule (12), domestic prices p = σσ−1rc
1+γso
1−s and export prices p∗ = σσ−1τrc
1+γso
1−s∗ .Hence, from demand (4), the relative quantity of domestic goods to foreign goods equals
x
x∗=
(p
p∗
)−σ=
(1
τ
1− s∗
1− s
)−σ(32)
From the market clearing condition,
Ns+ (I − 1)Ns∗ = 1
s+ (I − 1)s∗ = so
s∗ =so − sI − 1
(33)
Using (33) into (32) yields ( xx∗
) 1σ
=τ(1− s)1− s∗
=τ(1− s)1− so−s
I−1(34)
Plugging (34) and (33) into (31) yields our RMP condition
1− ss
1σ−1
=1
τ
1− s∗
s∗1
σ−1
1− ss
1σ−1
=1
τ
1− so−sI−1(
so−sI−1
) 1σ−1
(RMP)
The left hand side of this expression is decreasing in s (on the (0;1) interval from ∞ to 0)
30
and right hand side is increasing on the same interval (from 1τ1−soso
to ∞), so there exists aunique solution for s. Moreover, the right-hand side is decreasing in τ and increasing in so.Hence, along the RMP, ds
dso< 0, and a reduction in τ rotates the RMP curve clockwise.
Let us now derive the ZP curve. In the current model, the zero profit condition 16becomes
π = L
[s
(1− σ − 1
σ
1− s1 + γso
)+ (I − 1) s∗
(1− σ − 1
σ
1− s∗
1 + γso
)]= F
A reduction in iceberg trade costs, would increase the share of profits from export marketsand reduce the domestic share of profits. Using (33), and rearranging, we obtain our ZPcurve:
ZP (s, so) ≡ so +σ − 1
σ
1
1 + γso
[s
I − 1(Is− 2so)
]− σ − 1
σ
1
1 + γso
(so − 1
I − 1(so)2
)=F
L
Now let’s show that dsdso
< 0:
dG (s, so)
ds=σ − 1
σ
1
1 + γso
(2I
I − 1s− 2
I − 1so)> 0
as s ≥ so
I
dG (s, s0)
ds0= 1− σ − 1
σ
1
(1 + γs0)2
[1 +
2
I − 1s+ γ
I
I − 1s2 − 2
I − 1s0 − γ
1
I − 1(so)2
]as s ≤ s0
dG (s, s0)
ds0≥ 1− σ − 1
σ
1
I − 1
1 + γ (so)2
(1 + γso)2> 0
as γ > 0 and so ≤ 1.Then from implicit function theorem:
ds11ds0
= − dG/ds0dG/ds11
< 0
Let us now consider the effects of a reduction in τ on input prices. Plugging (??) and(16) into (18) we obtain:
r = γ̃1
1+γ
(L− F
s0
) γ1+γ
(35)
Hence, drdso
> 0 and consequently drdτ< 0, - higher trade costs lead to lower reward for the
factor.Let us now examine the effects of changes in τ on prices and quantities. Domestic prices
are given by:
p =σ
σ − 1rc
1 + γso
1− s
31
As drdτ< 0, ds
o
τ< 0, and ds
τ> 0 it follows that dp
dτhas an ambiguous sign. A reduction in trade
costs increases oligopsony power, but reduces oligopoly power, thus the ambiguous sign.The domestic supply of goods is
x =sL
p=σ − 1
σc
s (1− s)r (1 + γs)
as the numerator is increasing in τ and the denominator is decreasing, dxdτ> 0.
Recall that, r = γ̃[c 1so
(x+ (I − 1) τx∗)]γ
and using drdτ< 0, dx
dτ> 0, and dso
dτ< 0 we get
that dx∗
dτ< 0.
Export prices equal
p∗ =σ
σ − 1cτ
[r
1− s∗(1 + γso)
]Where the first term in square brackets is decreasing in τ and reflects olygopsonistic
effect, while the second term is increasing in τ and reflects the direct effect of higher tradecosts and lower market power in the destination market.
Notice, however, that even though the changes in prices are ambiguous, domestic salesare increasing in τ and export sales are decreasing:
d (px)
dτ> 0,
d (p∗x∗)
dτ< 0
as px = Ls and p∗x∗ = Ls∗.
6.1.4 Multiple Inputs
This section outlines an extension to the baseline model, in which firms purchase a numberof differentiated inputs and the purchase of differentiated inputs from abroad requires thepayment of an iceberg trade costs. As the number of subscripts increases quickly, we drop theorigin country subscript. Let us focus on the problem of firm f , which exports to j = 1, ..., Icountries.
To produce output xfj to country j, firm f uses k = 1, ..., K inputs. We assume thateach country supplies differentiated inputs, but we disregard the origin country subscript.Firm f uses ykfj units of input k to produce the output for destination j according to thefollowing production function:
xfj = f(ykfj) = f(y1fj, ..., yKfj) (36)
where we assume that f() is increasing, concave and exhibits constant returns to scale. ykfj
is the vector of inputs used in producing for destination j The total demand of firm f forinput k is ykf =
∑Ij=1 ykfj. Acquiring ykf units of the input is subject to an iceberg trade
32
cost tkf .9 The inverse demand for input k is given by
rk = γkYγk = γk
[∑v
tkvykv
]γ(37)
where v is the index of all firms using input k in production. Revenues are identical to thebaseline problem. To include iceberg trade costs, it suffices to divide revenues by τfj. Profitsare given by:
Πf =∑j
pfj(xfj)xfjτfj
−∑k
rktkvykv (38)
Πf =∑j
pfj(f(ykfj))f(ykfj)
τfj−∑k
γk
[∑v
tkv∑d
ykvd
]γtkf∑f
(ykfj) (39)
Firms maximize their profits by choosing ykfj. The first order conditions are given by:
σ − 1
στfjpfj(1− sfj)
∂ffj∂ykfj
= rktkf (1 + γsokf ) (40)
where
sokf =tkfykf∑v tkvykv
(41)
Multiplying both sides of 40 by ykfj, summing over inputs k, and using Euler’s theorem forhomogeneous of degree one functions we find:
σ − 1
στfjpfj(1− sfj)ykfj
∂ffj∂ykfj
= rktkfykfj(1 + γsokf )
σ − 1
στfjpfj(1− sfj)
∑k
ykfj∂ffj∂ykfj
=∑k
rktkfykfj(1 + γsokf )
σ − 1
στfjpfj(1− sfj)xfj =
∑k
rktkfykfj(1 + γsokf )
σ − 1
στfjpfj(1− sfj) =
∑k
rktkfykfjxfj
(1 + γsokf )
pfj =στfj
(σ − 1)(1− sfj)∑k
rktkfykfjxfj
(1 + γsokf )
Firm’s revenues in destination j are given by
pfj(xfj)xfjτfj
=σ
(σ − 1)(1− sfj)∑k
rktkfykfj(1 + γsokf ) (42)
9The proper notation for such iceberg trade cost would be: tkij where k is the input supplied from i usedby firms from j.
33
Let αk() denote the share of expenditures on input k over the total cost expenditures for theproduction of a good to a destination j, namely:
αk() =rktkfykfj∑u rutufyufj
(43)
Hence, since rktkfykfj = αk∑
u rutufyufj, firm’s revenues can be written as:
pfj(xfj)xfjτfj
=σ
(σ − 1)(1− sfj)∑k
αk∑u
rutufyufj(1 + γsokf )
=σ
(σ − 1)(1− sfj)∑u
rutufyufj∑k
αk(1 + γsokf )
Exploiting the definition of market share, we can simplify our cost to export to produce fordestination j.
pfj(xfj)xfjτfj
= sfjyjLj
σ
(σ − 1)(1− sfj)∑u
rutufykuj∑k
αk(1 + γsokf ) = sfjyjLj∑u
rutufyufj =σ − 1
σsfj(1− sfj)yjLj
1∑k αk(1 + γsokf )
Profits are then given by
Πf =∑j
pfjxfj −∑j
∑k
rktkfykfj − F =
=∑j
sfjyjLj
[1− σ − 1
σ
1− sfj∑k αk(1 + γsokf )
]− F
Let us re-write prices:
pfj =στfj
(σ − 1)(1− sfj)
∑u rutufyufjxfj
∑k
αk(1 + γsokf ) (44)
The average variable cost of selling to destination j is
AV Cfj =τfj∑
u rutufyufjxfj
(45)
Thus, prices are given by
pfj = AV Cfjσ
σ − 1
∑k αk(1 + γsokf )
1− sfj(46)
34
Cobb Douglas
Let us assume that the production function is Cobb-Douglas:
xfj = f(ykfj) = f(y1fj, ..., yKfj) =∏
yαkk∑k
αk = 1 (47)
Such an assumption implies that input cost shares (43) are constant. With a Cobb-Douglasutility function we can simplify the price equation, by finding a closed form expression forthe average variable costs.
Let us fix a firm f and a destination j, so as to drop firm and destination subscripts.Let us take the ratio between the FOC (40) of input k and input v (for the same firm anddestination). Assuming that the production function is Cobb-Douglas, we obtain
αkyvαvyk
=rktkrvtv
yk = yvαkrktk
rvtvαv
Substituting the demand for input k into the total variable cost function yields:∑k
rktkyk = yvrvtvαv
∑k
αk = yvrvtvαv
Substituting the demand for input k into the production function yields:
x =∏
yαkk = yvrvtvαv
∏(αkrktk
)αkHence, the average cost of the firm is a function of the iceberg trade cost of exporting to thedestination and a Cobb-Douglas aggregation of each input cost:
AV Cfj =τfj∑
u rutufyufjxfj
=τfj∏( αkrktkf
)αkFinally, our pricing equation simplifies to
pfj =τfj∏( αkrktkf
)αk σ
σ − 1
∑k αk(1 + γsokf )
1− sfj(48)
6.1.5 Multiple Industries
This section briefly outlines an extension to the baseline model, in which firms from differentindustries purchase the same input k. This extension informs us on the way to measureoligopsony power in the context of input-output linkages, as we do in the empirical analysis.
To simplify the notation let industries be denoted by subscript h = 1, ..., H. To bringthis to the data, we simply need to be careful with the definition of oligopsonist demand
35
share.
sokf =tkfykf∑v tkvykv
(49)
The demand share of a firm f for input k is the ratio between the firm’s demand and thetotal demand for the input. To simplify a bit the notation, let us only consider input k. Thetotal demand for the input from industry h is
Yh =∑f∈h
tfyf
The oligopsonist demand share is
sof =tfyf∑h Yh
=Yh∑h Yh︸ ︷︷ ︸
Industry Share
tfyfYh︸︷︷︸
Within-Industryso
(50)
6.2 Empirics
Table 2: Effect of one Standard Deviation Change in HIs on Prices
Baseline Adj Dest HHI US Exporting Adj Origin HHIOrigin HI 3.68%*** 3.63%*** 9.75%*** 0.95%***
(0.245) (0.245) (0.186) (0.017)Destination HI 0.756%*** 0.044% -0.19% 0.54%***
(0.252) (0.0016) (0.238) (0.245)
36